Preface | |

Preliminaries | |

Precalculus Review | |

PrecalculusReview II | |

The Cartesian Coordinate System | |

Straight Lines | |

Summary of Principal Formulas and Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

Functions, Limits, And The Derivative | |

Functions and Their Graphs | |

The Algebra of Functions | |

Functions and Mathematical Models | |

Portfolio | |

Using Technology: Finding the Points of Intersection of Two Graphs and Modeling | |

Limits | |

Using Technology: Finding the Limit of a Function | |

One-Sided Limits and Continuity | |

Using Technology: Finding the Points of Discontinuity of a Function | |

The Derivative | |

Using Technology: Graphing a Function and Its Tangent Line | |

Summary of Principal Formulas and Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

Differentiation | |

Basic Rules of Differentiation | |

Using Technology: Finding the Rate of Change of a Function | |

The Product and Quotient Rules | |

Using Technology: The Product and Quotient Rules | |

The Chain Rule | |

Using Technology: Finding the Derivative of a Composite Function | |

Marginal Functions in Economics | |

Higher-Order Derivatives | |

Using Technology: Finding the Second Derivative of a Function at a Given Point | |

Implicit Differentiation and Related Rates | |

Differentials | |

Using Technology: Finding the Differential of a Function | |

Summary of Principal Formulas and Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

Applications Of The Derivative | |

Applications of the First Derivative | |

Using Technology: Using the First Derivative to Analyze a Function | |

Applications of the Second Derivative | |

Using Technology: Finding the Inflection Points of a Function | |

Curve Sketching | |

Using Technology: Analyzing the Properties of a Optimization | |

UsingTechnology: Finding the Absolute Extrema of a Function | |

Optimization II | |

Summary of Principal Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

Exponential And Logarithmic Functions | |

Exponential Functions | |

Using Technology | |

Logarithmic Functions | |

Compound IntereSt. Using Technology: Finding the Accumulated Amount of an Investment, the Effective Rate of Interest, and the Present Value of an Investment | |

Differentiation of Exponential Functions | |

Using Technology | |

Differentiation of Logarithmic Functions | |

Exponential Functions as Mathematical Models | |

Portfolio | |

Using Technology: Analyzing Mathematical Models | |

Summary of Principal Formulas and Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

Integration | |

Antiderivatives and the Rules of Integration | |

Integration by Substitution | |

Area and the Definite Integral | |

The Fundamental Theorem of Calculus | |

Portfolio | |

Using Technology: Evaluating Definite Integrals | |

Evaluating Definite Integrals | |

Using Technology: Evaluating Integrals for Piecewise-Defined Functions | |

Area between Two Curves | |

Using Technology: Finding the Area between Two Curves | |

Applications of the Definite Integral to Business and Economics | |

Using Technology: Business and Economic Applications/Technology Exercises | |

Summary of Principal Formulas and Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

Additional Topics In Integration | |

Integration by Parts | |

Integration Using Tables of Integrals | |

Numerical Integration | |

Improper Integrals | |

Applications of Calculus to Probability | |

Summary of Principal Formulas and Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

Calculus Of Several Variables | |

Functions of Several Variables | |

Partial Derivatives | |

Portfolio | |

Using Technology: Finding Partial Derivatives at a Given Point | |

Maxima and Minima of Functions of Several Variables | |

The Method of Least Squares | |

Using Technology: Finding an Equation of Least-Squares Line | |

Constrained Maxima and Minima and the Method of Lagrange Multipliers | |

Double Integrals | |

Summary of Principal Formulas and Terms | |

Concept Review Questions | |

Review Exercises | |

Before Moving On | |

The Inverse of a Function | |

The Graphs of Inverse Functions | |

Functions That Have Inverses | |

Finding the Inverse of a Function | |

Indeterminant Forms and l'H?pital's Rule | |

The Indeterminant Forms 0/0 and 8/8 | |

Index | |

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